Topographically guided waves in a thin plate

The Kirchhoff plate theory is used to establish that a thin plate with a symmetric rectangular recess supports the propagation of a pure (i.e. non-radiating) flexural guided mode, which is localised in the vicinity of the topographic feature. The guided mode is shown to exist in the long-wave limit, as long as the wave-guiding recess is sufficiently wide. The plate with a symmetric rectangular ridge, on the other hand, is demonstrated to admit no guided waves in the same limit.